Ellipse Properties and Equations

Professor Dave explains how to graph ellipses, a type of conic section, by comparing them to circles. He defines ellipses using foci and discusses their properties, including axes of symmetry and vertices. The video covers the standard form of an ellipse's equation, how to graph it, and transformations. Ellipses are important in astronomy, as celestial bodies follow elliptical orbits.

What is the primary difference between a circle and an ellipse in terms of their formation as conic sections?

• Both are formed by a plane intersecting a cone parallel to its base.

• A circle is formed by a plane intersecting a cone parallel to its base, while an ellipse is formed by a plane intersecting a cone at an angle.

• A circle is formed by a plane intersecting a cone at an angle, while an ellipse is formed by a plane intersecting a cone parallel to its base.

• Both are formed by a plane intersecting a cone at an angle.

What is the constant property of an ellipse regarding its foci?

• The product of the distances from any point on the ellipse to the two foci is constant.

• The ratio of the distances from any point on the ellipse to the two foci is constant.

• The difference of the distances from any point on the ellipse to the two foci is constant.

• The sum of the distances from any point on the ellipse to the two foci is constant.

What is the length of the major axis of an ellipse in terms of A?

• A

• 2B

• 2A

• B

If an ellipse has A squared as 9 and B squared as 4, what are the values of A and B?

• A = 4, B = 9

• A = 3, B = 2

• A = 9, B = 4

• A = 2, B = 3

How do you determine the orientation of an ellipse based on its equation?

• If the term under X squared is greater, the ellipse is wider.

• If A is greater than B, the ellipse is taller.

• If B is greater than A, the ellipse is wider.

• If the term under Y squared is greater, the ellipse is wider.

What must be done to the equation of an ellipse if the number on one side is not equal to one?

• Add that number to both sides.

• Divide the entire equation by that number.

• Subtract that number from both sides.

• Multiply the entire equation by that number.

If the foci of an ellipse are at plus and minus one, and the vertices are at plus and minus two, what is the value of C?

• C = 3

• C = 1

• C = 4

• C = 2

How do the H and K values affect the graph of an ellipse?

• They determine the center of the ellipse.

• They determine the orientation of the ellipse.

• They determine the length of the axes.

• They determine the size of the ellipse.

What is the significance of ellipses in astronomy?

• They are used to determine the age of the universe.

• They are used to measure the distance between stars.

• They describe the orbits of celestial objects like planets and comets.

• They are used to calculate the speed of light.

What happens to the properties of an ellipse when it is transformed using H and K?

• The size of the ellipse changes.

• The center changes, but the axes and foci remain the same.

• The axes and foci change.

• The orientation of the ellipse changes.